A153407 Middle of 3 consecutive prime numbers such that p1*p2*p3+d1+d2+1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.

4817, 9011, 13841, 33797, 35027, 48341, 51581, 52163, 61331, 62213, 77747, 95111, 102611, 105143, 105683, 109673, 111773, 114797, 119759, 128237, 135389, 136733, 138683, 149213, 153953, 159791, 163211, 165443, 174851, 188681, 195977, 208037

Offset

1,1

Comments

4813*4817*4831+4+14=112002971670+-1=primes,...

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

lst={}; Do[p1=Prime[n]; p2=Prime[n+1]; p3=Prime[n+2]; d1=p2-p1; d2=p3-p2; a=p1*p2*p3+d1+d2+1; If[PrimeQ[a-1]&&PrimeQ[a+1], AppendTo[lst, p2]], {n, 8!}]; lst
cnpQ[{a_, b_, c_}]:=Module[{p=a*b*c+(b-a)+(c-b)+1}, And@@PrimeQ[p+{1, -1}]]; Transpose[Select[Partition[Prime[Range[20000]], 3, 1], cpnQ]][[2]] (* Harvey P. Dale, Jul 30 2013 *)

Crossrefs

Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153402, A153404, A153405, A153406

Sequence in context: A108010 A029553 A153406 * A339468 A252019 A299206

Adjacent sequences: A153404 A153405 A153406 * A153408 A153409 A153410

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 25 2008

Status

approved